Finite Group Databasebeta

C2×#13127317 #16741494

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13127317

Splittings

FittingC22×C13×#107 ⋊ C2
SylowC13 ⋊ C2×#3346

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#107C2
socleC23×C13C22×D4
prime radicalC2×#11719219C2
hypercenterC22×#107D13
hypocenterC13C2×#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

1942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

394 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1048143);